As used herein, the term "multilevel coded modulation" refers to arrangements in which input bits are divided into two or more groups which are individually encoded using respective redundancy codes. The encoded bits are then used jointly to select channel signal points from a predetermined signal constellation for transmission over a communication channel, such as a voiceband telephone channel. The principal advantage of adopting a multilevel coded modulation approach is that it provides the system designer with increased flexibility in designing a coding scheme which provides desired levels of error-rate performance, or "coding gain," while meeting various constraints on code complexity and decoding delay.
It also is desirable that modulation codes be invariant to rotations of the transmitted signal points by a phase ambiguity of the constellation. A code is said to be "rotationally invariant" when a valid sequence of signal points becomes another valid sequence of signal points after each point is rotated by a phase angle corresponding to a phase ambiguity of the constellation. Unless the codes are rotationally invariant, after such a rotation, the receiver will be unable to recover the bits that are associated with the signal points.
However, it is difficult to obtain rotational invariance in multilevel codes, especially where a large amount of coding gain is desired and when the constellation has more than two phase ambiguities.